Simplify the following expression: $ z = \dfrac{-2y + 10}{y - 3} + \dfrac{-9}{7} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-2y + 10}{y - 3} \times \dfrac{7}{7} = \dfrac{-14y + 70}{7y - 21} $ Multiply the second expression by $\dfrac{y - 3}{y - 3}$ $ \dfrac{-9}{7} \times \dfrac{y - 3}{y - 3} = \dfrac{-9y + 27}{7y - 21} $ Therefore $ z = \dfrac{-14y + 70}{7y - 21} + \dfrac{-9y + 27}{7y - 21} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{-14y + 70 - 9y + 27}{7y - 21} $ $z = \dfrac{-23y + 97}{7y - 21}$